Audio, video and computer magnetic recording tapes have magnetic recording layers that are given a smooth surface to provide higher sensitivity, particularly high output in high-frequency ranges. However, these smooth-surfaced magnetic recording tapes cannot be wound or rewound smoothly, and a variation in tape tension reduces the transport properties of the tape and causes fluctuations in tape output. Furthermore, these tapes are easily deformed or damaged. To eliminate these effects, a magnetic recording tape has been proposed that has a back coating on the surface of the nonmagnetic base opposite to that having a magnetic recording layer. However, a back coating thicker than 2.mu. cannot provide a higher S/N ratio. To produce a magnetic tape having improved S/N ratio and transport properties, a high-modulus back coating not thicker than 2.mu. must be used. But a high-modulus back coating does not adhere to the base intimately and easily sheds or comes off as dust to cause dropouts.